JERUSALEM/CAIRO, July 31 (Reuters) - Israel said on Tuesday it had received a letter from Egypt's President Mohamed Mursi indicating he wanted to work for peace in the Middle East, but Mursi's office later denied sending it.

An Israeli official, who asked to remain anonymous, said the denial was to be expected, due to the sensitivity of the issue.

Israeli President Shimon Peres's office said earlier on Tuesday he had received a letter from the Muslim Brotherhood's Mursi, in the first such missive to Israel since Mursi took office at the end of last month.

The letter, distributed by Peres's office, said: "I am looking forward to exerting our best efforts to get the Middle East peace process back to its right track in order to achieve security and stability for all peoples of the region, including (the) Israeli people."

Hours later, Mursi's spokesman branded the letter a fake.

"The letter that the media reported to have been sent from President Mursi to Israel was fake. President Mursi has not sent anything to Israel," spokesman Yasser Ali told Reuters.

An official from Peres's office said the letter was authentic.

"It was received by the Egyptian ambassador and handed over (to Peres's office). The denial was to be expected, given the letter's high publicity in Israeli and Egyptian media," the official said, speaking on condition of anonymity due to the sensitivity of the issue.

Peres's office had distributed a copy of the letter to media, as well as a copy of an Egyptian embassy message sent along with it. The official spoke on condition of anonymity due to the sensitivity of the issue.

The Egyptian embassy in Israel could not be reached for comment.

Last June, an Iranian news agency reported it spoke to Mursi a few hours before the announcement of the election results, but his spokesman then also denied that the interview took place.

A second Israeli official who spoke on condition of anonymity, described Mursi's letter as being one that gave "a general message with a positive spirit, but did not indicate any new direction" in bilateral relations.

ALARM IN ISRAEL OVER MURSI ELECTION

Politicians in Israel had expressed alarm in private over the election of the Muslim Brotherhood's Mursi in June's presidential vote and fear that over time their country's peace treaty with Egypt could be eroded.

Egypt's ousted President Hosni Mubarak had guaranteed the 1979 peace treaty with Israel for decades.

The Muslim Brotherhood is ideologically hostile to the Jewish state and linked to Hamas Islamists who run the Gaza Strip. Hamas refuses to recognise Israel's right to exist.

The presidency in Israel is a largely ceremonial post. Nobel peace-prize-winner Peres had sent Mursi two letters, his office said, one congratulating him for winning the vote and a second letter of greetings to mark the Muslim fasting month of Ramadan.

Prime Minister Benjamin Netanyahu had also sent Mursi a letter congratulating him on his electoral victory. He has not yet received a reply.

The Middle East peace process has stalled, with U.S.-brokered negotiations between Israel and the Palestinians breaking down in 2010, with no prospects of any swift resumption of talks. (Reporting and writing by Maayan Lubell in Jerusalem and Yasmine Saleh in Cairo, editing by Michael Roddy)